A Cyberinfrastructure (CI) is a combination of data resources, network protocols, computing platforms, and computational services that brings people, information, and computational tools together to perform science or other data-rich applications in this information-driven world. Most science domains adopt intrinsic geospatial principles (such as spatial constraints in phenomena evolution) for large amounts of geospatial data processing (such as geospatial analysis, feature relationship calculations, geospatial modeling, geovisualization, and geospatial decision support). Geospatial CI (GCI) refers to CI that utilizes geospatial principles and geospatial information to transform how research, development, and education are conducted within and across science domains (such as the environmental and Earth sciences). GCI is based on recent advancements in geographic information science, information technology, computer networks, sensor networks, Web computing, CI, and e-research/e-science. This paper reviews the research, development, education, and other efforts that have contributed to building GCI in terms of its history, objectives, architecture, supporting technologies, functions, application communities, and future research directions. Similar to how GIS transformed the procedures for geospatial sciences, GCI provides significant improvements to how the sciences that need geospatial information will advance. The evolution of GCI will produce platforms for geospatial science domains and communities to better conduct research and development and to better collect data, access data, analyze data, model and simulate phenomena, visualize data and information, and produce knowledge. To achieve these transformative objectives, collaborative research and federated developments are needed for the following reasons: (1) to address social heterogeneity to identify geospatial problems encountered by relevant sciences and applications, (2) to analyze data for information flows and processing needed to solve the identified problems, (3) to utilize Semantic Web to support building knowledge and semantics into future GCI tools, (4) to develop geospatial middleware to provide functional and intermediate services and support service evolution for stakeholders, (5) to advance citizen-based sciences to reflect the fact that cyberspace is open to the public and citizen participation will be essential, (6) to advance GCI to geospatial cloud computing to implement the transparent and opaque platforms required for addressing fundamental science questions and application problems, and (7) to develop a research and development agenda that addresses these needs with good federation and collaboration across GCI communities, such as government agencies, non-government organizations, industries, academia, and the public.